Infinite easier Waring constants for commutative rings. (English) Zbl 1222.11118
Any sum or difference of squares in any commutative ring can be written as \(x^2+y^2-z^2.\) The same is true for some exponents different from 2. The answer for cubes is unknown. The author gives a proof for the following result announced in 1978: If \(n \geq 2\), there is a commutative ring \(R\) with arbitrary long sums or differences of \(2^n\)-powers (which cannot be shortened).
Reviewer: L. N. Vaserstein (University Park)
MSC:
| 11P05 | Waring’s problem and variants |
References:
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